Best Known (81−50, 81, s)-Nets in Base 27
(81−50, 81, 114)-Net over F27 — Constructive and digital
Digital (31, 81, 114)-net over F27, using
- t-expansion [i] based on digital (23, 81, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(81−50, 81, 172)-Net in Base 27 — Constructive
(31, 81, 172)-net in base 27, using
- 15 times m-reduction [i] based on (31, 96, 172)-net in base 27, using
- base change [i] based on digital (7, 72, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 72, 172)-net over F81, using
(81−50, 81, 208)-Net over F27 — Digital
Digital (31, 81, 208)-net over F27, using
- t-expansion [i] based on digital (24, 81, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(81−50, 81, 244)-Net in Base 27
(31, 81, 244)-net in base 27, using
- 7 times m-reduction [i] based on (31, 88, 244)-net in base 27, using
- base change [i] based on digital (9, 66, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 66, 244)-net over F81, using
(81−50, 81, 16980)-Net in Base 27 — Upper bound on s
There is no (31, 81, 16981)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 87 307663 867621 732375 777559 664256 792504 665687 034759 537235 896073 506974 915146 033696 099973 172503 890412 370627 300333 233411 > 2781 [i]